Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Liouville theorem on integrable systems | Statement: [Liouville–Arnold theorem, alsoKnownAs, Liouville theorem on integrable systems]

Target entity: Liouville theorem on integrable systems
Context triple: [Liouville–Arnold theorem, alsoKnownAs, Liouville theorem on integrable systems]

• A. Liouville–Arnold theorem chosen
  The Liouville–Arnold theorem is a fundamental result in Hamiltonian mechanics that guarantees the integrability of a system with sufficiently many conserved quantities and describes its motion as quasi-periodic on invariant tori in phase space.
• B. Liouville's theorem in Hamiltonian mechanics
  Liouville's theorem in Hamiltonian mechanics states that the phase-space volume occupied by an ensemble of systems evolving under Hamiltonian dynamics is conserved over time, implying incompressible flow in phase space.
• C. Painlevé conjecture in celestial mechanics
  The Painlevé conjecture in celestial mechanics is a hypothesis about the possible occurrence of non-collision singularities—where bodies in an N-body gravitational system exhibit infinite behavior in finite time without actually colliding.
• D. Kolmogorov–Arnold–Moser theory
  Kolmogorov–Arnold–Moser theory is a fundamental result in dynamical systems that explains the persistence of quasi-periodic motions in nearly integrable Hamiltonian systems under small perturbations.
• E. Carathéodory–Jacobi–Lie theorem
  The Carathéodory–Jacobi–Lie theorem is a fundamental result in symplectic geometry and Hamiltonian mechanics that provides canonical local coordinates adapted to a given set of commuting functions.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.